HELP WITH THERMISTOR QUESTION!!!!!!

[littlecherry25]

THE DIAGRAM : a circuit with 12 V and a 4kiloOhm resistor and a thermistor (XY) in series

The thermistor is placed in warm water at an initial temp of 50 degrees Celsius and the voltage across XY is measured.

The water is now left to cool down to room temp at 20 degrees celsius

Kate wishes to maintain the water temp at 50 degrees celsius by a heating element placed into the water.

SHOULD KATE CONNECT THE HEATING ELEMENT ACROSS THE 4KILO-OHM RESISTOR OR XY ?

[appianway]

I'm not exactly sure what it'd look like with the diagram, but presumably a heating element uses the voltage drop across whatever it's connected to. You'd want this voltage drop to be smaller  when the external temperature is higher, and larger when the external temperature is higher.

Vout is proportional to the proportion of the resistance that the element composes, so you'd want it across something that has the majority of the resistance at low temperatures.

Therefore, presuming that the thermistor's resistance decreases with temperature, the element should be across XY.